Disclosed herein are methods, devices, apparatus, and articles of manufacture relating to the measurement or estimation of impedance properties, and/or their spatial distribution, in a conductive continuous medium or other conductive system presenting multiple conductive paths. Among other applications, the methods, apparatus, and articles of manufacture disclosed herein are well-suited for use in electrical impedance imaging and electrical impedance spectroscopy applications.
Many investigators have attempted to devise methods for producing images corresponding to the electrical impedance properties of a two or three dimensional object based upon measurements taken from electrodes placed around the outside of (and/or, optionally, at selected points within) the object. Potential applications of such a technology (referred to as electrical impedance tomography, or ‘EIT’) include medical imaging and diagnosis, and geological profiling.
Previous approaches to the problem have typically involved passing currents between various pairs of electrodes arrayed around the periphery of the object to be imaged. Multiple frequencies may be employed, and/or currents may be passed through multiple electrodes at once. Thus far, however, there has been relatively little success in reconstructing meaningful and reproducible images at a useful resolution, because of a seemingly intractable problem: currents applied through electrodes follow multiple paths of least resistance that themselves depend on the impedance characteristics of the object and are therefore unpredictable. Because of this, impedance imaging is in principle unlike other kinds of imaging such as computed tomography, where the measured signal represents an integral of the property being measured (such as density to x-rays) along a straight line path, which allows for straightforward reconstruction of a unique image from a number of such measurements along a variety of paths. In computed tomography where the measured data consists of line integrals of some physical property, reconstruction is accomplished using techniques that are well known to persons having ordinary skill in the art of imaging, such as back projection or Fourier analysis. Because the measurements sought to be used for impedance imaging are not line integrals, but rather represent the effect of the impedance properties of the object to be imaged along many paths at once, the problem of reconstructing an image from impedance measurements (often referred to as the ‘inverse EIT problem’) is one of a class of inverse problems known to be highly nonlinear, extremely ill-posed, and having many local optima.
Previous efforts to obtain useful images despite these drawbacks have typically focused on seeking ways to make the reconstruction problem less intractable—for example, in physiological imaging, the analysis may begin with an assumed mapping of the typical impedance properties and topography of the anatomical region sought to be measured. It may then be possible to construct an image at some resolution by using the assumed mapping to predict the path distribution of the applied currents, and use the results of the measurements to iteratively improve the mapping.
The present disclosure takes a different approach: in some embodiments, it seeks to make measurements in such a way that the current along a path of interest between electrodes can be estimated, thereby providing line integrals or estimates thereof from which images can be reconstructed directly using any of the many well-known line integral-based image reconstruction methods. More generally, methods and apparatus are disclosed for estimating spatially localized impedance properties along a conductive path of interest or in a localized region of interest.